4 questions from 2023
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\( S_1 \) and \( S_2 \) are two identical sound sources of frequency \( 656 \, \text{Hz} \). The source \( S_1 \) is located at \( O \) and \( S_2 \) moves anti-clockwise with a uniform speed \( 4\sqrt{2} \, \text{m s}^{-1} \) on a circular path around \( O \), as shown in the figure. There are three points \( P, Q \) and \( R \) on this path such that \( P \) and \( R \) are diametrically opposite while \( Q \) is equidistant from them. A sound detector is placed at point \( P \). The source \( S_1 \) can move along direction \( OP \).
[Given : The speed of sound in air is \( 324 \, \text{m s}^{-1} \) ]
When only \( S_2 \) is emitting sound and it is at \( Q \), the frequency of sound measured by the detector in \( {H_2} \) is_________.
A string of length \( 1 \, \text{m} \) and mass \( 2 \times 10^{-5} \, \text{kg} \) is under tension \( T \). When the string vibrates, two successive harmonics are found to occur at frequencies \( 750 \, \text{Hz} \) and \( 1000 \, \text{Hz} \). The value of tension \( T \) is _______ Newton.
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\( S_1 \) and \( S_2 \) are two identical sound sources of frequency \( 656 \, \text{Hz} \). The source \( S_1 \) is located at \( O \) and \( S_2 \) moves anti-clockwise with a uniform speed \( 4\sqrt{2} \, \text{m s}^{-1} \) on a circular path around \( O \), as shown in the figure. There are three points \( P, Q \) and \( R \) on this path such that \( P \) and \( R \) are diametrically opposite while \( Q \) is equidistant from them. A sound detector is placed at point \( P \). The source \( S_1 \) can move along direction \( OP \).
[Given : The speed of sound in air is \( 324 \, \text{m s}^{-1} \) ]
Consider both sources emitting sound. When \( S_2 \) is at \( R \) and \( S_1 \) approaches the detector with a speed \( 4 \, \text{m s}^{-1} \), the beat frequency measured by the detector is ______ \( \text{Hz} \).
An ideal gas is in thermodynamic equilibrium. The number of degree of freedom of a molecule of the gas is \( n \). The internal energy of one mole of the gas is \( U_{n} \) and the speed of sound in the gas is \( v_{n} \). At a fixed temperature and pressure, which of the following is the correct option?
